Signal Detection for Cognitive Radios With Smashed Filtering

Executive Summary

Compressed Sensing and the related recently introduced Smashed Filter are novel signal processing methods, which allow for low-complexity parameter estimation by projecting the signal under analysis on a random subspace. In this paper the Smashed Filter of Davenport et al. is applied to a principal problem of digital communications: pilot-based time offset and frequency offset estimation. An application, motivated by current Cognitive Radio research, is wide-band detection of a narrowband signal, e.g. to synchronize terminals without prior channel or frequency allocation. Smashed Filter estimation and maximum likelihood-based, uncompressed estimation for a signal corrupted by additive white Gaussian noise (Matched Filter estimation) are compared.